What are matter waves? Write the de Broglie relation and explain why the wave nature of a moving cricket ball is not observed, while that of an electron is.

1. 1 · State the hypothesis. de Broglie (1924): nature is symmetrical, so moving particles should also show wave nature; these waves are matter waves.
2. 2 · Write the relation. λ = h/p = h/mv.
3. 3 · Estimate for a ball. 0.15 kg at 20 m/s: λ ≈ 2.2 × 10⁻³⁴ m, far too small to show diffraction.
4. 4 · Estimate for an electron. At 7.28 × 10⁶ m/s: λ ≈ 0.1 nm, about the spacing of atoms in a crystal, so it can be measured.
5. 5 · Real life. Electron microscopes use electron waves.
6. 6 · Close in one line. So, wave nature matters only for very small particles.

Scoring tip: Show one quick estimate with numbers; it turns a 1-mark idea into a 3-mark answer.